The former welfare minister Lord Freud has admitted to MPs that administrative problems and design issues with universal credit are causing around one in four low-income tenants to run up rent arrears, putting them at risk of eviction.

Freud, who has overseen the development of universal credit over the past six years, also suggested that the long formal waiting times faced by claimants before they receive a first payment when they move on to the new benefit should be shortened.

However, Freud, who stepped down from the government in December, said the arrears problem was not as severe as claimed by councils and housing associations, who have reported that typically 85% of tenants on universal credit are behind with the rent.

“When I left … I was looking at figures that said there was a problem. There was a proportion of people – probably around a quarter – where universal credit was having an effect on arrears,” he told MPs on the work and pensions select committee.

He added: “There is an arrears issue, I’m not going to deny that, and things need to be done but it is not the dramatic story you are hearing from people.”

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The Guardian reported on Tuesday that thousands of council tenants on universal credit were at risk of eviction because of outstanding rent arrears caused or exacerbated by formal 42-day waits for a first benefit payment. Additional processing delays meant some claimants were waiting for up to 60 days.

One housing association said 80% of its low income tenants who moved onto universal credit reported that they did not have the financial resources to manage a 42-period without income, and many were routinely referred to food banks as a result.

The committee chairman, Frank Field, said he had seen capable people “reduced to tears” by the complexities of universal credit. “There are people who have never been in this situation of turmoil before who have found that universal credit was wrecking their lives.”

Asked what he would change about universal credit, Freud said some thought a 42-day wait was too long and suggested that a component of that wait, a seven-day benefit waiting period introduced by the Treasury in 2013, should be dropped. “Waiting days do not help in the introduction of universal credit.”

Freud told MPs that most of the tenants cited by housing associations were in arrears before they moved on to universal credit. He said Department of Work and Pensions’ (DWP) own research suggested that the prevalence of rent arrears among universal credit tenants declined after three months on the new system.

The DWP research he referred to was published over a year ago and referred to a phone survey of 1,800 benefit claimants conducted between November 2014 and March 2015. It shows that the percentage of the 900 universal credit claimants surveyed who said they were in rent arrears fell from 48% to 33% after three months.

Freud defended the delays that mean it is now six years behind its original schedule, and will not be fully rolled out until 2022. It was better to get things right than rush things to keep to an artificial programme, he said.

But Labour MP Neil Coyle said: “If you were in the private sector and you said you would do this at this cost and you come back two years later and say I’ve spent more than that and I cannot deliver it, you’d probably get the sack.”

Asked about the sometimes fractious relationship between the DWP and the Treasury over universal credit in recent years, Freud said: “There were times when one’s views about the Treasury were totally unprintable.”

However, he said the Treasury had at other times been supportive and praised the former Lib Dem MP Danny Alexander, who was chief secretary to the Treasury in the coalition government, for effectively saving universal credit when it’s future was in doubt in 2013.

Universal credit was introduced by the former work and pensions secretary, Iain Duncan Smith, in 2013 as a way of ensuring claimants would be better off in work than on benefits. However, Treasury cuts to work allowances within universal credit have reduced the incentive for some claimants to get a job and will leave 1.2 million working families worse off.